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Applied Mathematics and Mechanics(English Edition) 2002年第4期23卷 380-386页

作者：谢福鼎闫振亚张鸿庆 Department of Applied Mathematics Dalian University of Technology Dalian P R China

Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct met... 详细信息

关键词： nonlinear evolution equation FPU problem similarity reduction

STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR nonlinear DISSIPATIVE evolution equationS IN BANACH SPACE

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Journal of Computational Mathematics 2024年第2期42卷 337-354页

作者： Wansheng Wang Department of Mathematics Shanghai Normal UniversityShanghai 200234China

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.

关键词： nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability Convergence Banach space

New application to Riccati equation

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Chinese Physics B 2010年第8期19卷 88-95页

作者：套格图桑斯仁道尔吉李姝敏 College of Mathematical Science Inner Mongolia Normal University College of Mathematical Science Bao Tou Teachers' College

To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.

关键词： Riccati equation formula of nonlinear superposition nonlinear evolution equation exact solution

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

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Chinese Physics B 2014年第11期23卷 118-124页

作者：屈改珠张顺利李尧龙 Center for nonlinear Studies Department of Mathematics Northwest University School of Mathematics and Information Science Weinan Normal University

In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.

关键词： nonlinear evolution equation quadratic operator invariant subspace method blow-up solution

TAYLOR EXPANSION METHOD FOR nonlinear evolution equationS

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Applied Mathematics and Mechanics(English Edition) 2005年第4期26卷 522-529页

作者：何银年 Faculty of Science Xi'an Jiaotong University Xi'an 710049 P.R.China

A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.

关键词： nonlinear evolution equation Navier_Stokes equation Taylor expansion method convergence rate

Considering the heavy-quark distribution functions at low x

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Communications in Theoretical Physics 2023年第10期75卷 71-78页

作者： Elham Karampur G R Boroun Department of Physics Razi UniversityKermanshah 67149Iran

In this paper,we investigate the behavior of charm and bottom distribution functions at low x with respect to the parametrization of the gluon distribution function in the framework of the nonlinear Gribov–Levin–Ryskin–Mueller–Qiu,Zhu-Ruan-Shen(GLR-MQ-ZRS)evolution equation.Also,we solve the GLR-MQ-ZRS equation using the parametrization behavior of the gluon distribution function.The computed results are compared with the NNPDF3.0,CT14 and GRV92 collaborations.

关键词： nonlinear evolution equation heavy quark density low x

Constructing infinite sequence exact solutions of nonlinear evolution equations

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Chinese Physics B 2011年第11期20卷 23-33页

作者：套格图桑那仁满都拉 College of Mathematics Inner Mongolia University for Nationalities College of Mathematical Science Inner Mongolia Normal University College of Physics and Electronics Inner Mongolia University for Nationalities

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

关键词： first kind of elliptic function Backlund transformation nonlinear evolution equation new infinite sequence exact solutions

NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV equation WITH THREE ARBITRARY FUNCTIONS

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Applied Mathematics and Mechanics(English Edition) 2003年第11期24卷 1259-1263页

作者：张解放刘宇陆 Institute of nonlinear Physics Zhejiang Normal UniversityJinhua Zhejiang 321004 P.R.China Institute of Shanghai Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P.R.China Institute of Shanghai Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P. R. Chinahe truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.

The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.

关键词： variable coefficient nonlinear evolution equation soliton-like solution truncated expansion method

NOTE ON AN OPEN PROBLEM OF HIGHER ORDER nonlinear evolution equationS

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Acta Mathematica Scientia 2012年第6期32卷 2369-2376页

作者： Tujin Kim 常谦顺徐静 Institute of Mathematics Academy of Sciences of DPR of KoreaPyonyangDPR of Korea Institute of Applied Mathematics Academy of Mathematics and System SciencesChinese Academy of Sciences School of Statistics and Mathematics Zhejiang Gongshang University

In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example.

关键词： nonlinear evolution equation Cauchy problem higher order